Situation 3: There is no such thing as a "Double-Move" with a charge (without spending an Action Point). Double Move is shorthand for Move action + Standard Action downgraded to a Move. Since a Charge is a Standard Action you're short one (without an Action Point or some other method to get at least a Move action.)
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F. Randall FarmerOct 31 '12 at 0:24

1 Answer
1

Action: The check is usually part of a move action, but it can be part of any of the creature’s actions that involve the creature moving.

Therefore, in the general case you may absolutely jump as part of any action that involves moving, like a charge.

Looking at your scenarios, Situation 1 is true. You can jump as part of a move. Situation 2 is true, given that there is a square before the enemy, you may jump as part of the implicit move in the charge.

If the creature runs out of movement before landing, it also falls. However, if the jump was part of a move action, the creature can continue the jump as part of a double move, ending the first move action in midair and continuing the jump as part of the second move action. The creature makes a single Athletics check for the jump but can use squares of movement from both actions for it.

Which then simply requires us to satisfy ourselves as to the text of the Charge action:

... Move: The creature moves up to its speed toward the target. Each square of movement must bring the creature closer to the target, and the creature must end the move at least 2 squares away from its starting position.

Therefore, there is no implicit "move action" as subset of charge, the movement is an effect of the use of the power.

Your situation for "needing to charge the guy on the other side of a large pit" is... assuming you must charge them, instead of getting your portable arty to rain death on them and you keep off minions on this side, take a double-move to jump the chasm, then action-point charge. Just... don't fail the jump.